Hello, doctorgk!

A rectangle made of elastic material will be made into a cylinder by joining edges AD and BC.

To support the structure, a wire of fixed length L is placed along the diagonal of the rectangle.

Find the angle that will maximize the volume of the cylinder. Code:

D * - - - - - - - * C
| * |
| * |
| L * |
| * | L·sinθ
| * |
| * |
| * θ |
A * - - - - - - - * B
L·cosθ

We have: .

The height of the cylinder is: .

is the circumference of the circular base of the cylinder.

. .

The volume of a cylinder is: .

Substitute [1] and [2] into [3]: .

. . and we have: .

And **tha**t is the function to be maximized . . . good luck!